1. he came up with the systematization of analytic geomatry. He used algebra to halp him solve this. The algebra that he used was only demonstrated only in diagrams. He used analytic geometry to describe the shapes of verious polynomial. 2.The fact that he used just diagrams to show the shapes is a great deal of work. this was a good part to the math world it showed people the different shapes and the way they started solving geometry problems that had to do with shapes. this was a change and he is very well know for this. 3. Maria spoken many different language at a very young age. for most people it is hard for her to speak their own language at the age of nine. At the age of eleven maria was familiar with Greek German Spanish and Hebrew. 4. The Equation of a circle. This is helpful with the equation (x-h)^2+(y-k)^2=r^2 radius=r center (h,k) example: Find the equation of the circle with the center at (-1,2) and the radius 4, let h=-1 k=2 and r=4. [x-(-1)]^2+(y-2)^2=4^2 (x+1)^2+(y-2)^2=16 5. y-4=(-1/2)(x-(-2) y-4=(-1/2x)+1 y=-1/2x+5
April 29,2011 1. He was consider to be more of a scientist. He had a lot more to do with science than math. He used math to help him with his science work. He used many different conics in his work. He contibutes so much to science. He was the first to give a correct explanation of how the human eye worked. The volume of sloids that contributed to the world of calculus. He designed a new telescope. The Keplerian or astronomical telescope was the firat to use two convex lenses. He gave the first mathematical explanation of the close packing of equal sphers, which led to an explanation of the shape of celss of a honeycomb. These things are still important today most of this sutff is used in math lik calculus. Some of these things are also used in science. 2. You can use logarithm in chemistry to find pH. The logerithmic rule is used in algebra it states that Loga(uv)=Loga(u)+loga(v). Logarithms are used in measuring many physical quantities. the scale that is used to measure earthquakes, the Richter Scale, involves a logarithm. The scale that is used to measure the loudness of sound in decibles which involves logarithm. 3.the trou8ble i had was finding the slope. and then graphing it. For ex: m=155-79/11-7 you subtract the top and buttom and then you divide 4 into 76 and you get your slope. m=76/4 m=19 4. what i used was the system x + y = 2 and x - y = 8. x +y = 2 x - y = 8 this will be solved with the elimination method. Since the y are already positive and negative you will leave them out. Then just add them together. So you will end up with 2x=10. The you will divide by two and you will get x=5. that will be plugged into the first equation to find y. 5+y=2. 5.4x-3y>14 you would first add 3y to both sides. So you will end up with 4x>14+3y.Then you will divide by 4. Gets you x>14/4+3y/4.=x>7/2+3/4y. 5x+2y<12 you would first subtract 2y from both sides. This will give you 5x<12-2y. Then you eill divide the right side by 5. x<12/5-2y/5. that will be put like this x<12/5-2/5y. That is how you solve inequalities.
May 13, 2011 1. The Greeks highest level that was study was geometry. They only used two tools for everything they did with lines. they used a compass to draw circles and arces of circles.The ruler that they used was not to have any marks. They show you the basic four constructions that they worked with. The four constructions: 1) perpendicular bisector.(point is on construction line) 2) perpendicular from a point that is not on your construction line. 3) perpendicular with a given point. 4) constructing an anangle. 2. The octagon is used for stop sign. A triangle is use on the back of horse and buggies so people can see them. If you work in the shipping busines you will use an square (boxes). The highway signs that tell you where to go are rectangle. Sometime you can find pools that are trapezoid. 3. There was the Euclid's fifth postulate ("parallel postulate"). this states that if you have two lines are such that a third line can intersect them so the sum of the two interior angles. On on side that cross the parallel lines is less than two right angles. I would ask him how it made him feel when he finished all his project? People always have different feelings when they get something done after doing it for a long period of time. 4. The rhombus has four equal sides which can be a parallelogram. A parallelogram cant be a rhombus because all the sides are not equal.
2.The fact that he used just diagrams to show the shapes is a great deal of work. this was a good part to the math world it showed people the different shapes and the way they started solving geometry problems that had to do with shapes. this was a change and he is very well know for this.
3. Maria spoken many different language at a very young age. for most people it is hard for her to speak their own language at the age of nine. At the age of eleven maria was familiar with Greek German Spanish and Hebrew.
4. The Equation of a circle. This is helpful with the equation (x-h)^2+(y-k)^2=r^2 radius=r center (h,k) example:
Find the equation of the circle with the center at (-1,2) and the radius 4, let h=-1 k=2 and r=4.
[x-(-1)]^2+(y-2)^2=4^2
(x+1)^2+(y-2)^2=16
5. y-4=(-1/2)(x-(-2)
y-4=(-1/2x)+1
y=-1/2x+5
April 29,2011
1. He was consider to be more of a scientist. He had a lot more to do with science than math. He used math to help him with his science work. He used many different conics in his work. He contibutes so much to science. He was the first to give a correct explanation of how the human eye worked. The volume of sloids that contributed to the world of calculus. He designed a new telescope. The Keplerian or astronomical telescope was the firat to use two convex lenses. He gave the first mathematical explanation of the close packing of equal sphers, which led to an explanation of the shape of celss of a honeycomb. These things are still important today most of this sutff is used in math lik calculus. Some of these things are also used in science.
2. You can use logarithm in chemistry to find pH. The logerithmic rule is used in algebra it states that Loga(uv)=Loga(u)+loga(v). Logarithms are used in measuring many physical quantities. the scale that is used to measure earthquakes, the Richter Scale, involves a logarithm. The scale that is used to measure the loudness of sound in decibles which involves logarithm.
3.the trou8ble i had was finding the slope. and then graphing it. For ex:
m=155-79/11-7 you subtract the top and buttom and then you divide 4 into 76 and you get your slope.
m=76/4
m=19
4. what i used was the system x + y = 2 and x - y = 8.
x +y = 2
x - y = 8
this will be solved with the elimination method. Since the y are already positive and negative you will leave them out. Then just add them together. So you will end up with 2x=10. The you will divide by two and you will get x=5. that will be plugged into the first equation to find y. 5+y=2.
5.4x-3y>14
you would first add 3y to both sides. So you will end up with 4x>14+3y.Then you will divide by 4.
Gets you x>14/4+3y/4.=x>7/2+3/4y.
5x+2y<12
you would first subtract 2y from both sides. This will give you 5x<12-2y. Then you eill divide the right side by 5. x<12/5-2y/5.
that will be put like this x<12/5-2/5y.
That is how you solve inequalities.
May 13, 2011
1. The Greeks highest level that was study was geometry. They only used two tools for everything they did with lines. they used a compass to draw circles and arces of circles.The ruler that they used was not to have any marks. They show you the basic four constructions that they worked with.
The four constructions:
1) perpendicular bisector.(point is on construction line)
2) perpendicular from a point that is not on your construction line.
3) perpendicular with a given point.
4) constructing an anangle.
2. The octagon is used for stop sign. A triangle is use on the back of horse and buggies so people can see them. If you work in the shipping busines you will use an square (boxes). The highway signs that tell you where to go are rectangle. Sometime you can find pools that are trapezoid.
3. There was the Euclid's fifth postulate ("parallel postulate"). this states that if you have two lines are such that a third line can intersect them so the sum of the two interior angles. On on side that cross the parallel lines is less than two right angles.
I would ask him how it made him feel when he finished all his project? People always have different feelings when they get something done after doing it for a long period of time.
4. The rhombus has four equal sides which can be a parallelogram. A parallelogram cant be a rhombus because all the sides are not equal.